A simple magnifier gives the maximum angular magnification when it forms a virtual image at the near point of the eye instead of at infinity. For simplicity, assume that the magnifier is right up against the eye, so that distances from the magnifier are approximately the same as distances from the eye. 

(a) For a magnifier with focal length f, find the object distance p such that the image is formed at the near point, a distance N from the lens. 

(b) Show that the angular size of this image as seen by the eye is

where h is the height of the object.

(c) Now find the angular magnification and compare it to the angular magnification when the virtual image is at infinity.

0 = h(N + f) Nf